Question

P
1. In the figure, M is the
midpoint of QR.
PRQ = 90°
Prove that
PQ2 = 4PM? - 3PR2.
R​

Answer 1

Answer:

Explanation:According to Pythagoras theorem in ∆PRM

PM²= PR²+ RM²

RM²=PM²-PR²  

In ∆PRQ

PR²= RQ²+PQ²

PQ²= PR ²+ (RM+MQ)²

PQ²= PR ²+ (RM+RM)²

PQ²= PR ²+ (2RM)²

PQ²= PR ²+ (4RM)²

PQ²= PR ²+ 4(PM²-PR²)  

PQ²= PR ²+ 4PM²- 4PR²

PQ²= 4PM²- 3PR²